CN103365203A - Control apparatus, lithography apparatus, and method of manufacturing article - Google Patents

Abstract

The present invention provides a control apparatus, a lithography apparatus, and a method of manufacturing an article. The control apparatus includes a feed-forward controller configured to perform feed-forward control of a controlled object, the apparatus being configured to obtain a first response data sequence of the controlled object measured by applying a first manipulated variable to the controlled object, and determining, assuming that a second response data sequence of the controlled object to be obtained if a second manipulated variable data sequence, obtained by respectively multiplying the first manipulated variable by gains as variables which can vary with time, is applied to the controlled object, is expressed as a linear combination of the first response data sequence with the gains as coefficients of the liner combination, the gains so that a discrepancy between the second response data sequence and a target data sequence falls within a tolerance.

Description

The method of control device, offset printing device and manufacturing article

Technical field

The present invention relates to the method for control device, offset printing device and manufacturing article.

Background technology

Figure 24 is the block diagram of typical 2DOF control system.With reference to Figure 24, provide from input (desired value) r to the transport function of exporting (controlled variable) y by following formula:

$y=(\frac{\mathrm{KP}}{1+\mathrm{KP}}+\frac{\mathrm{FP}}{1+\mathrm{KP}})r...\left(1\right)$

Wherein, first of the right side is feedback (FB) item, and second of the right side is feedforward (FF) item.Difference between desired value r and the controlled variable y is departure e, and the 2DOF control system is intended to departure e is made as zero (making departure e close to 0).

With reference to equation (1), from for the y=r of F=1/P as seen, when the transport function (FF gain) of FF controller is defined as the inverse function of transport function (characteristic) of controll plant, can obtain desirable desired value response (minimizing of departure).In this way, the performance of desired value response is determined in the pin-point accuracy modeling of controll plant (using transport function and numerical value that the pin-point accuracy of controll plant is represented).

To the controll plant modeling time, controll plant is the known polynomial expression that is represented as Laplace operator s usually.As long as controll plant can be the polynomial expression of Laplace operator s by Precise Representation, then its inverse function also can be expressed as the polynomial expression of Laplace operator s, allows thus best FF control.At the movable body control field, reported the FF(of the FF of the single order differential (speed) by the target location and second-order differential (acceleration) in addition, the FF of three rank differential (jerk) of target location and the FF of quadravalence differential) improve the desired value response.Yet, be difficult to the characteristic entirely accurate of controll plant be expressed as the polynomial expression of Laplace operator s.In addition, although the polynomial modeling technique that uses Laplace operator s is not only arranged, and various modeling techniques are earlier attempted, but controll plant all can't be by entirely accurate ground modeling, so can't prevent modeling error in any these modeling techniques.

The characteristic variations of controll plant is a factor of modeling error.For example, be used for the moving body control of mobile vehicle, the weight of the characteristic load of controll plant and the state on road surface and change.Japanese Patent Publication No.2009-237916 has proposed to prepare the technology that some models select based on real response suitable model, rather than uses exclusively a model for controll plant, deals with this variation of the characteristic of controll plant.

In the control system take the 2DOF control system as representative, as mentioned above, the performance of desired value response depends on the accuracy to the controll plant modeling.Therefore, along with the required performance of control system becomes higher, controll plant need to be modeled with pin-point accuracy more, thereby sizable load is applied on the modelling operability.By the technology described among the Japanese Patent Publication No.2009-237916 to modeling error reduce limited by pre-prepd model.

Summary of the invention

For example the invention provides favourable control device aspect the reducing of departure.

According to a first aspect of the invention, a kind of control device is provided, comprise feedforward controller, this feedforward controller is configured to carry out the feedforward control of controll plant, described control device is configured to: obtain by controll plant being applied the first response data sequence of the controll plant that the first performance variable measures, if and the second performance variable data sequence of obtaining by the gain of the first performance variable be multiply by respectively as the variable that can change in time of supposition is applied in controll plant and the second response data sequence of the controll plant that will obtain is represented as the first response data sequence and as the linear combination of the gain of the coefficient of linear combination, determine gain so that the difference between the second response data sequence and the target data sequence falls in the permission, and feedforward controller is configured to generate feedforward operation variable data sequence for controll plant based on determined gain.

According to a second aspect of the invention, provide a kind of and formed the offset printing device of pattern at object, described offset printing device comprises: adjustment equipment is configured to adjust the state of object; With above-mentioned control device, this control device is configured to control the adjustment equipment as controll plant.

According to a third aspect of the invention we, provide a kind of method of making article, described method comprises: use flat plate printing apparatus to form pattern at object; And the object that has formed pattern above processing makes article, and wherein, described flat plate printing apparatus comprises: adjustment equipment is configured to adjust the state of object; And control device, be configured to control the adjustment equipment as controll plant, wherein said control device comprises the feedforward controller of the feedforward control that is configured to carry out controll plant, described control device is configured to: obtain by controll plant being applied the first response data sequence of the controll plant that the first performance variable measures, if and the second performance variable data sequence of obtaining by the gain of the first performance variable be multiply by respectively as the variable that can change in time of supposition is applied in controll plant and the second response data sequence of the controll plant that will obtain is represented as the first response data sequence and as the linear combination of the gain of the coefficient of linear combination, determine gain so that the difference between the second response data sequence and the target data sequence falls in the permission, and feedforward controller is configured to generate feedforward operation variable data sequence for controll plant based on determined gain.

From referring to the description of accompanying drawing to exemplary embodiment, further feature of the present invention will become clear.

Description of drawings

Fig. 1 is the synoptic diagram that the configuration of exposure device according to an aspect of the present invention is shown.

Fig. 2 A and 2B are position and the departure difference time-sequence curve charts over time that Substrate table is shown.

Fig. 3 A and 3B are response over time the time-sequence curve charts respectively that the feedforward operation variable that puts on Substrate table and Substrate table be shown.

Fig. 4 A and 4B are virtual responsive over time the time-sequence curve charts respectively that the feedforward operation variable that puts on virtually Substrate table and Substrate table be shown.

Fig. 5 A and 5B are the departure time-sequence curve charts over time that Substrate table is shown.

Fig. 6 A is that respectively over time time-sequence curve chart of the position of the thrust that puts on Substrate table and Substrate table and departure is shown to 6C.

Fig. 7 A is the departure time-sequence curve chart over time that illustrates for the Substrate table of every group of coordinate of Substrate table to 7C.

Fig. 8 illustrates Fig. 7 A under the overlaying state to the curve map of the departure shown in the 7C.

Fig. 9 A is the feedforward operation variable time-sequence curve chart over time that puts on Substrate table that illustrates for every group of coordinate of Substrate table to 9C.

Figure 10 A is the departure time-sequence curve chart over time that illustrates when Substrate table when Fig. 9 A is applied in Substrate table respectively to the feedforward operation variable shown in the 9C to 10C.

Figure 11 A is the departure time-sequence curve chart over time that illustrates when Substrate table when Fig. 9 A is applied in Substrate table respectively to the feedforward operation variable shown in the 9C to 11C.

Figure 12 A is the time-sequence curve chart that illustrates for the variation of the departure of the Substrate table of each group in front four groups of coordinates of Substrate table and feedforward operation variable to 12D.

Figure 13 A is the time-sequence curve chart that illustrates for the variation of the departure of the Substrate table of each group in four groups of coordinates of residue of Substrate table and feedforward operation variable to 13D.

Figure 14 A is Figure 12 A to be shown to the result's of the component decomposition in time of the feedforward operation variable shown in the 12D curve map to 14D.

Figure 15 A is Figure 13 A to be shown to the result's of the component decomposition in time of the feedforward operation variable shown in the 13D curve map to 15D.

Figure 16 A is that the approximate error time-sequence curve chart over time that produces for the result that the feedforward operation variable is similar to of every group of coordinate of Substrate table and when feedforward operation variable approximate is shown to 16D.

Figure 17 A is to illustrate for the result that the feedforward operation variable is similar to of every group of coordinate of Substrate table and the approximate error time-sequence curve chart over time that produces to feedforward operation variable approximate the time to 17D.

Figure 18 A is departure and the approximate feedforward operation variable time-sequence curve chart over time that illustrates for the Substrate table of each group in front four groups of coordinates of Substrate table to 18D.

Figure 19 A is departure and the approximate feedforward operation variable time-sequence curve chart over time that illustrates for the Substrate table of each group in four groups of coordinates of residue of Substrate table to 19D.

Figure 20 is the block diagram of temperature control system.

Figure 21 A is temperature over time the curve map respectively that object and controll plant when the temperature control system shown in Figure 20 is carried out given operation be shown to 21C.

Figure 22 A is the benchmark rate of heat flow that puts on controll plant to be shown respectively and temperature and the temperature variation time-sequence curve chart over time of controll plant when the benchmark rate of heat flow is applied in controll plant to 22C.

Figure 23 A and 23B illustrate the feedforward operation variable that puts on controll plant and the temperature time-sequence curve chart over time of controll plant.

Figure 24 is the block diagram of 2DOF control system.

Embodiment

Hereinafter with reference to accompanying drawing the preferred embodiments of the present invention are described.Notice that identical Reference numeral represents identical member, and will not provide the description of its repetition in the drawings.

The＜the first embodiment 〉

Fig. 1 is the synoptic diagram that the configuration of exposure device 1 according to an aspect of the present invention is shown.Exposure device 1 as by step-scan mechanism with the pattern transfer of mask (master) the offset printing device to the substrate.Yet exposure device 1 can also adopt stepping repeat mechanism or other exposure mechanisms.

Exposure device 1 comprises: lamp optical system 104, and it uses the optical illumination mask 106 from light source 102; Mask platform 108, it moves when keeping mask 106; And projection optics system 110, its pattern with mask 106 projects on the substrate 112.Exposure device 1 also is included in Substrate table 114, mobile mirror 116, laser interferometer 118 and the opertaing device (control device) 120 that moves when keeping substrate 112.

Light source 102 uses excimer laser, as has the KrF excimer laser of the wavelength of about 248nm, perhaps has the ArF excimer laser of the wavelength of about 193nm.Yet the type of light source 102 and quantity are not limited especially, and have for example F of the wavelength of about 157nm ₂Laser instrument can be used as light source 102.

Lamp optical system 104 usefulness are from the irradiation mask 106 of light source 102.Lamp optical system 104 for example comprises the beam-shaping optical system that the light from light source 102 is formed and forms a large amount of secondary light sources comes optical integrator with uniform Illumination Distribution irradiation mask 106.

Mask 106 has the pattern that will be transferred on the substrate 112, and masked 108 keeps and drive.Its pattern of masked 106() light of institute's diffraction projects on the substrate 112 via projection optics system 110.Mask 106 and substrate 112 are arranged with the optical conjugate relation.Because exposure device 1 is the step-scan exposure device, its pattern by synchronous scanning mask 106 with the pattern transfer of mask 106 to substrate 112.

Mask platform 108 comprises for keeping mask 106(to clamp by attracting) the mask chuck, and can be on X, Y and Z direction and mobile about the sense of rotation of each axle.Notice that mask 106 or the direction of scanning of substrate 112 in its face are defined as Y-axis, the direction vertical with this direction of scanning is defined as X-axis, and the direction vertical with the plane of mask 106 or substrate 112 is defined as Z axis.

Projection optics system 110 projects the pattern of mask 106 on the substrate 112.Projection optics system 110 can use dioptric system, reflected refraction system or reflecting system.

Substrate 112 is substrates that projection (transfer printing) has the pattern of mask 106 on it.Substrate 112 is coated with resist (emulsion).Substrate 112 comprises wafer, glass plate and other substrates.

Substrate table 114 comprises for keeping substrate 112(to clamp by attracting) the substrate chuck, and can be on X, Y and Z direction and mobile about the sense of rotation of each axle.Mobile mirror 116 is fixed to Substrate table 114, and is used to detect by laser interferometer 118 position and the speed of Substrate table 114.Substrate table 114 usefulness adjust equipment, and it cooperates to adjust the state of substrate 112 with opertaing device 120.

The operation of opertaing device 120 control (whole) exposure devices 1.The operation that opertaing device 120 control examples are associated such as the synchronous scanning with mask platform 108 and Substrate table 114.In the present embodiment, opertaing device 120 comprises use Substrate table 114 as feedforward controller 122 and the feedback controller 124 of controll plant, and storer 126, and control Substrate table 114.Feedforward controller 122 puts on Substrate table 114 as controll plant with the feedforward operation variable, to carry out the feedforward control of Substrate table 114, so that the output of Substrate table 114 response has desired value (target data).Feedback controller 124 is carried out the FEEDBACK CONTROL of Substrate table 114 in order to reduce the output response of Substrate table 114 and the error between the desired value.Storer 126 is data storage unit that storage is associated with the control of Substrate table 114.In the present embodiment, especially, storer 126 storages for example put on the feedforward operation variable of Substrate table 114 from feedforward controller 122.The below is description control equipment 120, more specifically, and the control of 122 pairs of Substrate tables 114 of forward direction controller.

Fig. 2 A is the position time-sequence curve chart over time that Substrate table 114 is shown.Fig. 2 B is departure (that is, the skew between the position of Substrate table 114 and target location (the desired value)) time-sequence curve chart over time that Substrate table 114 is shown.Fig. 2 A illustrates the position of Substrate table 114 and at horizontal ordinate is shown the time at ordinate.In addition, Fig. 2 B illustrates the departure of Substrate table 114 and at horizontal ordinate is shown the time at ordinate.

As can be seen from Figure 2A, Substrate table 114 begins mobile in the moment 0, and arrives the target location near the moment 300.Yet, shown in Fig. 2 B, in the moment about 300, still have the larger departure of Substrate table 114, thereby Substrate table 114 does not arrive the target location fully.The exposure device that is used for producing the semiconductor devices need to be at the nanometer scale Substrate table that aligns.Therefore, in this case, the moment that can begin exposure-processed is the moment subsequently in the stable moment of the departure of Substrate table 114 450.

Fig. 3 A illustrates feedforward (FF) performance variable (the first performance variable) time-sequence curve chart over time that puts on Substrate table 114.Fig. 3 B is response (the first response data sequence) time-sequence curve chart over time that Substrate table 114 when the FF performance variable that Substrate table 114 applied shown in Fig. 3 A is shown.Fig. 3 A illustrates the FF performance variable and at horizontal ordinate is shown the time at ordinate.In addition, Fig. 3 B illustrates the response of Substrate table 114 and at horizontal ordinate is shown the time at ordinate.

Can find out that from Fig. 3 A and 3B when the FF performance variable that is represented by near the square waves the moment 280 was applied in Substrate table 114, Substrate table 114 illustrated impulse response reaction (response characteristic) simultaneously.FF performance variable shown in Fig. 3 A and the 3B and response have respectively by the laser interferometer 118 that the performance variable that puts on Substrate table 114 is detected or sensor (not shown) measures the actual measured value of (actual measurement).

Fig. 4 A illustrates the FF performance variable time-sequence curve chart over time that puts on virtually Substrate table 114.Fig. 4 B is the virtual responsive time-sequence curve chart over time that Substrate table 114 when the virtual FF performance variable that Substrate table 114 applied shown in Fig. 4 A is shown.Fig. 4 A illustrates the FF performance variable and at horizontal ordinate is shown the time at ordinate.In addition, Fig. 4 B illustrates the response of Substrate table 114 and at horizontal ordinate is shown the time at ordinate.

With situation about considering shown in Fig. 4 A, wherein, than late constantly 100 the moment 380 places of the moment 280, the FF performance variable shown in Fig. 3 A is put on Substrate table 114 virtually in conduct.In this case, shown in Fig. 4 B, as the response of Substrate table 114, obtain conduct than late constantly 100 the virtual responsive of the response of the Substrate table 114 shown in Fig. 3 B.This is that namely, the response characteristic of Substrate table 114 is assumed that and always keeps identical because put on the performance variable of Substrate table 114 and the response of Substrate table 114 is assumed that to have linear relationship.In other words, the response shown in Fig. 3 B is assumed to be at the moment 380 acquisition of the FF performance variable shown in Fig. 3 A when the moment 380 is applied in Substrate table 114.

Allow Δ f (t) be the FF performance variable shown in Fig. 3 A, and Δ y (t) is the response shown in Fig. 3 B, then the FF performance variable shown in Fig. 4 A can be represented as Δ f (t-100), and the response shown in Fig. 4 B can be represented as Δ y (t-100).Although based on obtaining the constantly virtual responsive of the Substrate table 114 at 380 places in the constantly response (actual measured value) of the Substrate table 114 at 280 places in the present embodiment, can be similarly the moment 281,282 ..., the 280+n place obtains the virtual responsive of Substrate table 114.

Next with consider to put on Substrate table 114 the FF performance variable gain (amplitude) and for the response of the Substrate table 114 of this gain.Notice that gain is can time dependent variable.In this embodiment, as mentioned above, be measured for the response Δ y (t) of FF performance variable Δ f (t).Therefore, have linear relationship as long as put on the performance variable of Substrate table 114 and the response of Substrate table 114, then expectation obtains response (the second response data sequence) the g Δ y (t) for performance variable (the second performance variable data sequence) g Δ f (t).When using the time migration of FF performance variable, this sets up too, thereby expectation obtains the response g100 Δ y (t-100) for FF performance variable g100 Δ f (t-100).

The below will based on the concept of the present invention of more early describing, describe the control of the Substrate table 114 of being carried out by feedforward controller 122 in more detail in conjunction with actual data stream.

At first, when Substrate table 114 not being applied the FF performance variable, obtain result's (actual measured value) of the departure e (t) of measurement Substrate table 114.Determine to carry out the time interval (moment 331 to 420 in the present embodiment) of exposure-processed, and the departure data from the time interval of departure e (t) extraction exposure-processed.At this moment, suppose that sampling instant is 1, then extract departure data e according to following formula ₀90 samplings:

$e_0={\left[\begin{array}{cccc}{e}_1& {\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA00002983525500063.png,HDA00002983525500072.png"\; state="\{\{state\}\}">e</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& e_{90}\end{array}\right]}^T...\left(2\right)$

At given time Substrate table 114 is applied FF performance variable Δ f (t), and obtain to measure the result's (actual measured value) for the response Δ y (t) of FF performance variable Δ f (t), shown in Fig. 3 A and 3B.Extract response data the time interval of exposure-processed from the response Δ y (t) of Substrate table 114.The response data y that extracts in this mode is described by following formula ₀:

${\mathrm{<figure-callout\; id="0"\; label="y"\; filenames="HDA00002983525500051.png,HDA00002983525500052.png"\; state="\{\{state\}\}">y</figure-callout>}}_0={\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00002983525500052.png,HDA00002983525500081.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{1,0}}& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA00002983525500063.png,HDA00002983525500072.png"\; state="\{\{state\}\}">\; <figure-callout\; id="0"\; label="y"\; filenames="HDA00002983525500051.png,HDA00002983525500052.png"\; state="\{\{state\}\}">y</figure-callout>\; </figure-callout>}}_{\mathrm{2,0}}& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{<figure-callout\; id="90"\; label="y"\; filenames="HDA00002983525500211.png,HDA00002983525500212.png"\; state="\{\{state\}\}">y</figure-callout>}}_{\mathrm{90,0}}\end{array}\right]}^T...\left(3\right)$

In above situation, obtain actual measured value as data, and in following situation, produce virtual data.Suppose after a sampling that obtains to be applied with FF performance variable Δ f (t), when similar FF performance variable is put on Substrate table 114, to obtain similarly to respond, and the response of acquisition is defined as y ₁Similarly, the response after two samplings, three sampling responses afterwards ..., and n sampling response afterwards is defined as y ₂, y ₃..., y _n, we have:

As mentioned above, when controll plant (Substrate table 114) when being linear, be represented as g Δ y (t) for the response of FF performance variable g Δ f (t).Therefore, allow g _nBe the gain of the FF performance variable after n the sampling, we have:

Estimate the response of the Substrate table 114 when all the FF performance variables after n sampling are applied in Substrate table 114.When the response data from the time interval of the exposure-processed of this response extraction is defined as Y, response data Y be n response and.Then, we have:

In order to eliminate departure (departure data e in the time interval of exposure-processed by Substrate table 114 being applied the FF performance variable ₀), response data Y only need to equal departure data e ₀Therefore, use as shown in the formula the pseudo inverse matrix that provides, obtain the gain g of (determining) FF performance variable _n:

e ₀=Y

Fig. 5 A and 5B illustrate when the FF performance variable of determining according to thus obtained gain (that is, by with FF performance variable Δ f (t+t _n) multiply by definite gain g _nAnd the FF performance variable g that obtains _nΔ f (t+t _n)) departure of this Substrate table 114 when being applied in Substrate table 114.Fig. 5 A is the departure time-sequence curve chart over time the interval that is illustrated in from the moment 0 to the moment 600, and Fig. 5 B is the amplified curve figure of the departure of the Substrate table 114 in the interval (that is, the time interval of exposure-processed) that illustrates from the moment 331 to the moment 420.Fig. 5 A and 5B illustrate the departure of Substrate table 114 at ordinate, and at horizontal ordinate are shown the time.In addition, with reference to Fig. 5 A and 5B, solid line represents the departure of the Substrate table 114 when Substrate table 114 not being applied above-mentioned FF performance variable, and dotted line represents the departure of the Substrate table 114 when Substrate table 114 is applied above-mentioned FF performance variable.

Obvious from Fig. 5 B, the departure in the time interval of exposure-processed when as in the present embodiment, Substrate table 114 being applied the FF performance variable than little when Substrate table 114 not being applied the FF performance variable.More specifically, when not having the FF performance variable to be applied in Substrate table 114, near the departure the moment 331 is too large so that can't allow exposure-processed.On the other hand, as in the present embodiment, when the FF performance variable is applied in Substrate table 114, drop within the permission in order to allow exposure-processed thereby near the departures the moment 331 are fully stable.

By this layout, in the present embodiment, based on the result of the response of measuring the Substrate table 114 when Substrate table 114 being applied FF performance variable (benchmark performance variable), obtain to put on the FF performance variable of Substrate table 114 at every turn, and need not the Substrate table 114 as controll plant is carried out modeling.In other words, suppose that then this gain is confirmed as so that the difference between the response of Substrate table 114 and the desired value (target data sequence) falls in the permission when the linear combination of Substrate table 114 being used the response of Substrate table 114 when having each gain as the benchmark performance variable of coefficient and be represented as the response of Substrate table 114.Generate FF performance variable (feedforward operation variable data sequence) based on the gain of determining for Substrate table 114.Therefore, in the present embodiment, can control Substrate table 114 in pin-point accuracy ground, and can not produce modeling load or modeling error.

In addition, in the present embodiment, suppose that the response characteristic of Substrate table 114 always keeps identical, then obtain for all responses among the response g Δ y (t) of FF performance variable g Δ f (t) (output response) by calculating.Yet in fact, it is identical that the response characteristic of Substrate table 114 does not always keep.Under these circumstances, can obtain for some responses the response g Δ y (t) of FF performance variable g Δ f (t) from measurement result (actual measured value), obtain remaining response by calculating simultaneously.Perhaps, can obtain for all responses the response g Δ y (t) of FF performance variable g Δ f (t) from measurement result (actual measured value).

The＜the second embodiment 〉

Fig. 6 A is the thrust time-sequence curve chart over time that the Substrate table 114 that puts on exposure device 1 is shown.Fig. 6 B is the position time-sequence curve chart over time that Substrate table 114 when the thrust that Substrate table 114 applied as shown in Figure 6A is shown.Fig. 6 C is the departure time-sequence curve chart over time that Substrate table 114 when the thrust that Substrate table 114 applied shown in Fig. 6 A is shown.Fig. 6 A illustrates the thrust [N] that puts on Substrate table 114 at ordinate, and at horizontal ordinate is shown the time [s].Fig. 6 B illustrates the position [m] of Substrate table 114 at ordinate, and at horizontal ordinate is shown the time [s].Fig. 6 C illustrates the departure [m] of Substrate table 114 at ordinate, and at horizontal ordinate is shown the time [s].Fig. 6 A obtains when Substrate table 114 is in the first coordinate time to each data shown in the 6C.Notice that the coordinate of Substrate table 114 refers to expression as the coordinate (they typically are the coordinate (x, y) in the above-mentioned X-Y-Z orthogonal coordinate system, but are not limited to this example) of the position of the Substrate table 114 of controll plant.

As can be seen from Figure 6A, the interval from the moment 0 to the moment 0.03, Substrate table 114 is applied in positive thrust, therefore accelerates.It can also be seen that from Fig. 6 A the interval from the moment 0.03 to the moment 0.06, Substrate table 114 is applied in negative thrust, therefore slows down.As can be seen from Figure 6B, Substrate table 114 arrives the target location near the moment 0.06.Can find out from Fig. 6 C, during Substrate table 114 moves, occured high to approximately ± departure of 200 μ m, and departure be stabilized to constantly 0.06 and subsequently the time be engraved in the degree that does not observe departure in the scale of this curve map.

Fig. 7 A illustrates the departure of Substrate table 114 when the coordinate time that changes Substrate table 114 applies thrust shown in Fig. 6 A to Substrate table to 7C.Fig. 7 A illustrates when Substrate table 114 to be in over time time-sequence curve chart of the first coordinate time departure (with shown in Fig. 6 C identical).Fig. 7 B illustrates when Substrate table 114 to be in the second coordinate time departure time-sequence curve chart over time.Fig. 7 C illustrates departure time-sequence curve chart over time when Substrate table 114 is in three-dimensional.Fig. 8 is illustrated in constantly 0.08 to be engraved in Fig. 7 A under the overlaying state to subsequently the time to the amplified curve figure of the departure shown in the 7C.Fig. 7 A illustrates the departure [m] of Substrate table 114 to 7C and Fig. 8 at ordinate, and at horizontal ordinate is shown the time [s].From Fig. 7 A to 7C and Fig. 8 can find out that when the changes in coordinates of Substrate table 114, even Substrate table 114 is applied identical thrust, the departure of Substrate table 114 (its shape) also changes.

Fig. 9 A illustrates to 9C and uses the result who puts on the FF performance variable of Substrate table 114 according to the method (that is, not having modeling) of the first embodiment for every group of coordinate acquisition of Substrate table 114.In this case, carry out the time interval of exposure-processed, that is, make the departure of Substrate table 114 keep less time interval to be set as from constantly 0.1 to constantly 0.2.Fig. 9 A illustrates when Substrate table 114 to be in the FF performance variable time-sequence curve chart over time that the first coordinate time puts on Substrate table 114.Fig. 9 B illustrates when Substrate table to be in the FF performance variable time-sequence curve chart over time that the second coordinate time puts on Substrate table 114.Fig. 9 C illustrates the FF performance variable time-sequence curve chart over time that puts on Substrate table 114 when Substrate table is in three-dimensional.Fig. 9 A illustrates the FF performance variable [N] that puts on Substrate table 114 to 9C at ordinate, and at horizontal ordinate is shown the time [s].Can find out that from Fig. 9 A to 9C optimum FF performance variable changes respectively organizing in the coordinate of Substrate table 114.

Figure 10 A illustrates the departure of the Substrate table 114 when Substrate table 114 being applied Fig. 9 A to the FF performance variable shown in the 9C to 11C to 10C and 11A.Figure 10 A illustrates when Substrate table 114 to be in the first coordinate time departure time-sequence curve chart over time.Figure 10 B illustrates when Substrate table 114 to be in the second coordinate time departure time-sequence curve chart over time.Figure 10 C illustrates departure time-sequence curve chart over time when Substrate table 114 is in three-dimensional.Figure 11 A is illustrated in constantly 0.08s and the amplified curve figure of the departure shown in Figure 10 A at place constantly subsequently.Figure 11 B is illustrated in constantly 0.08s and the amplified curve figure of the departure shown in Figure 10 B at place constantly subsequently.Figure 11 C is at moment 0.08s and the amplified curve figure of the departure shown in Figure 10 C at place constantly subsequently.Figure 10 A illustrates the departure [m] of Substrate table 114 and at horizontal ordinate is shown the time [s] at ordinate to 11C to 10C and 11A.In addition, with reference to Figure 10 A to 10C and 11A to 11C, solid line represents the departure of the Substrate table 114 when Substrate table 114 not being applied Fig. 9 A to the FF performance variable shown in the 9C, and dotted line represents the departure of the Substrate table 114 when Substrate table 114 being applied Fig. 9 A to the FF performance variable shown in the 9C.

As from Figure 10 A to 10C and 11A obvious to 11C, from 0.1 departure to 0.2 the interval constantly constantly when Fig. 9 A is applied in Substrate table 114 to the FF performance variable shown in the 9C than little when described performance variable is not applied in Substrate table 114.More specifically, when Fig. 9 A was applied in Substrate table 114 to the FF performance variable shown in the 9C, the departure the interval from the moment 0.1 to the moment 0.2 was fully stable to drop in the permission.

Utilize this operation, even the response characteristic of Substrate table 114 (output response characteristic) changes in each group coordinate, also can pin-point accuracy ground control Substrate table 114.More specifically, can be by obtaining FF performance variable (best FF performance variable) for each moving area in Substrate table 114 mobile ranges (for example, each standard is taken (shot) zone), pin-point accuracy ground control Substrate table 114.Yet, the response characteristic of Substrate table 114 is usually not only according to the coordinate of Substrate table 114 but also change according to the moving state of Substrate table 114 (comprise the mobile number of times of Substrate table 114 and mobile historical, take layout and target location profile (pattern that the target location changed according to the time)).Under these circumstances, can obtain the FF performance variable by each moving state for Substrate table 114, come pin-point accuracy ground control Substrate table 114.In other words, only need to obtain to put on for each behaviour in service (response characteristic of Substrate table 114 changes according to behaviour in service) the FF performance variable (or gain) of Substrate table 114.

The＜the three embodiment 〉

For Substrate table 114 respectively organize coordinate, Figure 12 A illustrate to 12D and 13A to 13D the Substrate table 114 when Substrate table 114 is not applied the FF performance variable departure, put on the departure of FF performance variable and the Substrate table when Substrate table is applied in the FF performance variable 114 of Substrate table 114.Note, use the method (that is, not having modeling) according to the first embodiment, obtain the FF performance variable.In this case, carry out the time interval of exposure-processed, that is, the departure of Substrate table 114 be kept less time interval be set as from constantly 0.1 to constantly 0.2.Figure 12 A is to illustrate when Substrate table 114 to be in respectively first, second, third and departure (not having the FF performance variable), FF performance variable and departure (the FF performance variable is arranged) time-sequence curve chart over time during 4-coordinate to 12D.Figure 13 A is departure (not having the FF performance variable), FF performance variable and departure (the FF performance variable is arranged) time-sequence curve chart over time that is in respectively the 5th, the 6th, the 7th and the 8th coordinate time when Substrate table 114 to 13D.Figure 12 A illustrates the departure (the FF performance variable is arranged) [m] of the departure (not having the FF performance variable) [m] of Substrate table 114, the FF performance variable [N] that puts on Substrate table 114 and Substrate table 114 at ordinate according to the order from left curve map to 13D to 12D and 13A.In addition, Figure 12 A illustrates time [s] at horizontal ordinate to 13D to 12D and 13A in all curve maps.

From Figure 12 A to 12D and 13A can find out that to 13D along with the changes in coordinates of Substrate table 114, the departure of Substrate table 114 (its shape) also changes, thereby the FF performance variable that puts on Substrate table 114 changes, as mentioned above.From Figure 12 A to 12D and 13A can find out to 13D, when the FF performance variable is applied in Substrate table 114, from constantly 0.1 departure to 0.2 the interval constantly is fully stable to fall in the permission.

In exposure device, a substrate comprises 100 or more shooting area, so need to be when moving (scanning) Substrate table the pattern of the mask at 100 of Substrate table or more different coordinates place be carried out transfer printing.Therefore, when the FF performance variable that puts on Substrate table when respectively organizing of Substrate table changes in the coordinate, exposure device must have the storer of storage 100 or more FF performance variables.

Because exposure device has multilevel hierarchy computer organization, so when as long as stratum level does not need to be considered, it is relatively easy that 100 or more FF performance variable are stored in the storer.Yet, Substrate table is spent the very short time from move to next coordinate to position fixing (approximately 0.1[s]), therefore be difficult to the FF performance variable of changing at ensuing coordinate from higher stratum level at this time durations.Therefore, the required data of control Substrate table are stored in the computing machine (storer) of lower grade, the computing machine of this lower grade (storer) has limited memory span, so 100 of current extremely difficult storages or more FF performance variable.

Therefore, will the data volume that how to reduce the FF performance variable be described in the present embodiment.In this case, here will (with reference to Figure 12 A to 12D and 13A to 13D) description eight FF performance variables corresponding with eight groups of coordinates (the first to the 8th coordinate) of Substrate table 114 as example.Figure 14 A illustrates respectively Figure 12 A to the result of the component decomposition of the FF performance variable shown in the 12D to 14D, and Figure 15 A illustrates respectively Figure 13 A to the result of the component decomposition of the FF performance variable shown in the 13D to 15D.In the present embodiment, use characteristic value (eigenvalue) decomposition is decomposed into each component with the FF performance variable.Figure 14 A is illustrated in the sequential of a plurality of components (component data sequence) A, the B, C, D, E, F, G and the H that comprise in the FF performance variable in the left side to 14D and 15A to 15D, and a plurality of component A are shown to the intensity of H on the right side.With reference to the right side of Figure 14 A to 14D and 15A to 15D, with eight intensity drawn (that is, having eight drawing) that the FF performance variable is corresponding.Therefore, eight FF performance variables equal the linearity of a plurality of component A to H and a plurality of component A to the product of the intensity of H with.

Detailed description is provided the Eigenvalues Decomposition of the example that the component of FF performance variable decomposes.At first, make f ₁(t) to f ₈(t) be the data (time series data) of eight FF performance variables, the matrix F by these data acquisitions of cascade is provided by following formula:

$F=\left[\begin{array}{cccccccc}{f}_1\left(t\right)& f_2\left(t\right)& f_3\left(t\right)& f_4\left(t\right)& f_5\left(t\right)& f_6\left(t\right)& f_7\left(t\right)& f_8\left(t\right)\end{array}\right]$

$=\left[\begin{array}{cccccccc}{f}_{11}& f_{12}& f_{13}& f_{14}& f_{15}& f_{16}& f_{17}& f_{18}\\ f_{21}& f_{22}& f_{23}& f_{24}& f_{25}& f_{26}& f_{27}& f_{28}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ f_{n1}& f_{n2}& f_{n3}& f_{n4}& f_{n5}& f_{n6}& f_{n7}& {\mathrm{<figure-callout\; id="8"\; label="f\; n"\; filenames="HDA00002983525500141.png,HDA00002983525500151.png"\; state="\{\{state\}\}">f</figure-callout>}}_n\end{array}\right]...\left(8\right)$

In addition, provided the covariance matrix C of matrix F by following formula:

C=F ^T*F ...(9)

By Eigenvalues analysis, obtain to satisfy matrix V and the D of following formula:

CV=VD ...(10)

Then, provide the matrix Z that represents eight orthogonal vectors by following formula:

$=\left[\begin{array}{cccccccc}{z}_{11}& z_{12}& z_{13}& z_{14}& z_{15}& z_{16}& z_{17}& z_{18}\\ z_{21}& z_{22}& z_{23}& z_{24}& z_{25}& z_{26}& z_{27}& z_{28}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ z_{n1}& z_{n2}& z_{n3}& z_{n4}& z_{n5}& z_{n6}& z_{n7}& {\mathrm{<figure-callout\; id="8"\; label="z\; n"\; filenames="HDA00002983525500141.png,HDA00002983525500151.png"\; state="\{\{state\}\}">z</figure-callout>}}_n\end{array}\right]...\left(11\right)$

Notice that when vector was orthogonal, a vector can not be expressed as the addition of other vectors.

Utilize this operation, can derive eight orthogonal vectors from eight FF performance variables.

Eight FF performance variables are decomposed into orthogonal vector.In other words, eight FF performance variable f ₁(t) to f ₈(t) be expressed as the linearity of orthogonal vector and (with orthogonal vector z ₁(t) to z ₈(t) multiply by that given proportionality constant obtains the result's and).Allow the G be matrix of coefficients, we have:

$\left[\begin{array}{cccccccc}{f}_{11}& f_{12}& f_{13}& f_{14}& f_{15}& f_{16}& f_{17}& f_{18}\\ f_{21}& f_{22}& f_{23}& f_{24}& f_{25}& f_{26}& f_{27}& f_{28}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ f_{n1}& f_{n2}& f_{n3}& f_{n4}& f_{n5}& f_{n6}& f_{n7}& {\mathrm{<figure-callout\; id="8"\; label="f\; n"\; filenames="HDA00002983525500141.png,HDA00002983525500151.png"\; state="\{\{state\}\}">f</figure-callout>}}_n\end{array}\right]$

$=\left[\begin{array}{cccccccc}{z}_{11}& z_{12}& z_{13}& z_{14}& z_{15}& z_{16}& z_{17}& z_{18}\\ z_{21}& z_{22}& z_{23}& z_{24}& z_{25}& z_{26}& z_{27}& z_{28}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;& \&CenterDot;\\ z_{n1}& z_{n2}& z_{n3}& z_{n4}& z_{n5}& z_{n6}& z_{n7}& z_{n8}\end{array}\right]\left[\begin{array}{cccccccc}{g}_{11}& g_{12}& g_{13}& g_{14}& g_{15}& g_{16}& g_{17}& g_{18}\\ g_{21}& g_{22}& g_{23}& g_{24}& g_{25}& g_{26}& g_{27}& g_{28}\\ g_{31}& g_{32}& g_{33}& g_{34}& g_{35}& g_{36}& g_{37}& g_{38}\\ g_{41}& g_{42}& g_{43}& g_{44}& g_{45}& g_{46}& g_{47}& g_{48}\\ g_{51}& g_{52}& g_{53}& g_{54}& g_{55}& g_{56}& g_{57}& g_{58}\\ g_{61}& g_{62}& g_{63}& g_{64}& g_{65}& g_{66}& g_{67}& g_{68}\\ g_{71}& g_{72}& g_{73}& g_{74}& g_{75}& g_{76}& g_{77}& g_{78}\\ g_{81}& g_{82}& g_{83}& g_{84}& g_{85}& g_{86}& g_{87}& {\mathrm{<figure-callout\; id="88"\; label="g"\; filenames="HDA00002983525500211.png"\; state="\{\{state\}\}">g</figure-callout>}}_{88}\end{array}\right]$

$F=\mathrm{ZG}...\left(12\right)$

Therefore, when the inverse matrix of Z was multiply by on the both sides of equation (12), acquisition matrix of coefficients G was:

G=Z ^-1F ...(13)

Utilize this operation, eight FF performance variables can be decomposed into quadrature component A to H.

Note, from Figure 14 A to 14D and 15A can find out to H that to the component A in the left side of 15D the component A except component G and H is quite little to F.This means and only to represent (being similar to) eight FF performance variables by component G and H.

Respectively organize coordinate for Substrate table 114, Figure 16 A illustrates the result's (approximate FF performance variable) who the FF performance variable that puts on Substrate table 114 is similar to by component G and H to 16D and 17A to 17D, and the approximate error of generation when approximate to the FF performance variable (between FF performance variable and the approximate FF performance variable poor).Figure 16 A is to illustrate when Substrate table 114 to be in respectively first, second, third and approximate FF performance variable and approximate error time-sequence curve chart over time during 4-coordinate to 16D.Figure 17 A is to illustrate when Substrate table 114 is in respectively the 5th, the 6th, the 7th and the 8th coordinate time to be similar to FF performance variable and approximate error time-sequence curve chart over time to 17D.Figure 16 A illustrates FF performance variable [N] and the approximate error [N] that puts on Substrate table 114 at ordinate to 17D to 16D and 17A in order from left curve map, and at horizontal ordinate is shown the time [s].In addition, to 16D and 17A to the left curve map shown in the 17D, solid line represents not by component G and the approximate FF performance variable of H, and dotted line represents by component G and the approximate approximate FF performance variable of H with reference to Figure 16 A.From Figure 16 A to 16D and 17A can find out that to the left curve map shown in the 17D FF performance variable (solid line) and approximate FF performance variable (dotted line) almost are equal to each other, thereby their difference (approximate error) can't be observed.From Figure 16 A to 16D and 17A it can also be seen that to the left curve map shown in the 17D approximate error is very little.

For Substrate table 114 respectively organize coordinate, Figure 18 A illustrate to 18D and 19A to 19D the Substrate table 114 when Substrate table 114 not being applied the FF performance variable departure, put on the departure of approximate FF performance variable and the Substrate table 114 when Substrate table 114 being applied approximate FF performance variable of Substrate table 114.In this case, approximate FF performance variable is the result who Figure 12 A is similar to the FF performance variable shown in the 13D to 12D and 13A by component G and H.Figure 18 A is to illustrate when Substrate table 114 to be in respectively first, second, third and departure (not having the FF performance variable), approximate FF performance variable and departure (approximate FF performance variable is arranged) time-sequence curve chart over time during 4-coordinate to 18D.Figure 19 A is to illustrate when Substrate table 114 to be in respectively the 5th, the 6th, the 7th and the 8th coordinate time departure (not having the FF performance variable), approximate FF performance variable and departure (approximate FF performance variable is arranged) time-sequence curve chart over time to 19D.Figure 18 A illustrates the departure (approximate FF performance variable is arranged) [m] of the departure (not having the FF performance variable) [m] of Substrate table 114, approximate FF performance variable [N] and Substrate table 114 successively at ordinate from left curve map to 18D and 19A to 19D, and at horizontal ordinate is shown the time [s].

From Figure 18 A to 18D and 19A can find out to 19D, even Substrate table 114 has been applied approximate FF performance variable, from constantly 0.1 departure to 0.2 the interval constantly is fully stable to fall in the permission.This is because as mentioned above, and the approximate error that is produced when the FF performance variable that puts on Substrate table 114 is approximate by component H and G is very little.

Therefore, at exposure device 1(opertaing device 120) in, replacing FF performance variable itself, storer 126 is respectively organized coordinate for Substrate table 114, and storage is for principal component and intensity thereof that the FF performance variable is similar to.In other words, when the linearity of the product by a plurality of different components and their intensity with when coming the FF performance variable be similar to, 126 of storeies need to store a plurality of components and their intensity.In the present embodiment, can reduce memory load, this is because 126 of storeies need two component G of storage FF performance variable and H and two component G and H for the intensity of respectively organizing coordinate of Substrate table 114, and does not store eight FF performance variables.

In addition, storer 126 organizes respectively for Substrate table 114 that coordinate storage is included in component (principal component) in the FF performance variable and the situation of their intensity is to provide as the example in the present embodiment.Yet storer 126 can operate to store component (principal component) and their intensity that is included in the FF performance variable for each of moving substrate platform 114.

The above has described the present invention's (that is, supposing that controlled variable is the position of Substrate table) with the Substrate table of exposure device as the example of controll plant.Yet controll plant is not limited to Substrate table, and the present invention need can be applied to the various controll plants of feedforward control.Below will be applied to the situation of temperature control system (that is, controlled variable is the temperature of controll plant) to the present invention as example.

The＜the four embodiment 〉

Figure 20 is the block diagram of temperature control system.Temperature control system shown in Figure 20 is used as such control system: its rate of heat flow q[J/s] as input, temperature y[K] as output, and according to the temperature of controlling controll plant from the rate of heat flow of temperature controller.Controll plant is by thermal resistance R ₁[K/W] with have a temperature T ₁The object OB of [K] ₁Contact, and by thermal resistance R ₂[K/W] with have a temperature T ₂The object OB of [K] ₂Contact.Therefore, heat is to pass through controll plant and object OB ₁And OB ₂Between temperature difference respectively divided by thermal resistance R ₁And R ₂And the flow rate that obtains is from object OB ₁And OB ₂Flow to controll plant.In other words, controll plant is from temperature controller reception rate of heat flow q, from object OB ₁Receive rate of heat flow (T ₁-y)/R ₁, and from object OB ₂Receive rate of heat flow (T ₂-y)/R ₂When the flow rate of the heat that flows to controll plant by with respect to time integral the time, obtain to flow into the heat of controll plant.As the thermal capacitance C[J/K of the heat that flows into controll plant divided by controll plant] time, the temperature of acquisition controll plant.

Figure 21 A is illustrated in object OB after the given operation of temperature control system to 21C ₁And OB ₂Variation with the temperature of controll plant.Figure 21 A is object OB ₁Temperature T ₁Time dependent time-sequence curve chart.Figure 21 B illustrates object OB ₂Temperature T ₂Time-sequence curve chart over time.Figure 21 C is the temperature y time-sequence curve chart over time that controll plant is shown.Figure 21 A illustrates object OB at ordinate ₁Temperature T ₁[K] and is shown at horizontal ordinate the time [s].Figure 21 B illustrates object OB at ordinate ₂Temperature T ₂[K] and is shown at horizontal ordinate the time [s].Figure 21 C illustrates the temperature y[K of controll plant at ordinate] and at horizontal ordinate is shown the time [s].In addition, in this case, R1=R2=10[K/W] and C=10[J/K].

In this embodiment, suppose object OB when temperature control system is carried out identical operation ₁And OB ₂Temperature always with identical rate variation (Figure 21 A and Figure 21 B), so by controll plant being applied the temperature variation that the FF performance variable reduces controll plant.

At first, when when controll plant not being applied the situation lower operating temps control system of FF performance variable, the temperature variation of controll plant is as shown in Figure 21 C.Make e (t) be the temperature variation of controll plant, we have:

e(t)=[e ₀ e ₁ … e ₁₀₀] ^T ...(14)

In order to obtain the temperature characterisitic of controll plant from actual measured value, as shown in Figure 22 A, applying benchmark rate of heat flow q ₀(t) operating temperature control system the time.Allow y ₀(t) be the temperature variation of controll plant this moment, then by Δ y ₀(t)=y ₀(t)-e (t) provides for benchmark rate of heat flow q ₀The temperature variation of controll plant (t) (with reference to Figure 22 B and 22C).Therefore, for gain g ₀Rate of heat flow g ₀q ₀(t) response g ₀Δ y ₀(t) obtainedly be:

Δy ₀(t)=[y ₀ y ₁ … y ₁₀₀] ^T ...(15)

g ₀Δy ₀(t)=g ₀[y ₀ y ₁ … y ₁₀₀] ^T

In the present embodiment, only obtain data (actual measured value) by these two operations.In addition, in this embodiment, from moment 0[s] to 5[s constantly] the interval with 2[J/s] be applied to controll plant as the reference rate of heat flow.Notice that Figure 22 A illustrates the benchmark rate of heat flow time-sequence curve chart over time that puts on controll plant.Figure 22 B is the time-sequence curve chart that the temperature of controll plant when the benchmark rate of heat flow that controll plant is applied in shown in Figure 22 A is shown.Figure 22 C is the temperature time-sequence curve chart over time that controll plant when the benchmark rate of heat flow that controll plant is applied in shown in Figure 22 A is shown.Figure 22 A illustrates rate of heat flow q[J/s at ordinate], and at horizontal ordinate is shown the time [s].Figure 22 B illustrates the temperature [K] of controll plant at ordinate, and at horizontal ordinate is shown the time [s].Figure 22 C illustrates the temperature variation Δ y[K of controll plant at ordinate], and at horizontal ordinate is shown the time [s].

Provide when constantly 1 with gain g by following formula ₁Controll plant is applied benchmark rate of heat flow q ₀(t) the FF performance variable q the time ₁(t):

q ₁(t)=g ₁q ₀(t-1) ...(16)

Therefore, provide for FF performance variable q by following formula ₁(t) response Δ y ₁(t):

Δy ₁(t)=g ₁Δy ₀(t-1)=g ₁[0 y ₀ L y ₉₉] ^T ...(17)

Similarly, make q ₂(t) to q ₁₀₀(t) constantly 2 to 100 sentencing gain g for working as ₂To g ₁₀₀Apply respectively benchmark rate of heat flow q ₀(t) the FF performance variable the time, we have:

In addition, allow Δ y ₂(t) to Δ y ₁₀₀(t) be respectively for FF performance variable q ₂(t) to q ₁₀₀(t) response, we have:

With reference to equation (18) and (19), when controll plant being applied all FF performance variable g ₀q ₀To g ₁₀₀q ₀, the response Y (t) of controll plant is all response g ₀y ₀To g ₁₀₀y ₀Summation, as shown in the formula providing:

With reference to equation (20), the response Y (t) of controll plant is based on gain matrix G and the response matrix Y for the response acquisition of benchmark rate of heat flow ₀Product.Note, with the first embodiment in identical mode obtain gain (gain matrix G) for the temperature variation that reduces controll plant.More specifically, according to following formula, gain only needs obtained for so that controll plant becomes opposite in sign with the temperature variation e (t) of controll plant when controll plant not being applied the FF performance variable for the symbol of the response Y (t) of FF performance variable:

Y(t)=Y ₀G=-e(t) ...(21)

Therefore, multiply by response matrix Y when the both sides of equation (21) ₀Pseudo inverse matrix the time, the gain (gain matrix G) that be used for to reduce the temperature variation of controll plant can obtained (determining) be:

G＝-Y ₀ ^-1e(t) ...(22)

When obtaining gain in this way, provide FF performance variable g by following formula ₀q ₀(t), q ₁(t) ..., q ₁₀₀(t) summation Q (t):

Therefore, by using gain g _nMultiply by FF performance variable q _nCan obtain FF performance variable g _nq _n(that is, Q (t)) is as the best FF performance variable that puts on controll plant.

Figure 23 A illustrates according to thus obtained gain and definite FF performance variable.In addition, Figure 23 B illustrates the temperature of the controll plant when the FF performance variable that controll plant applied shown in Figure 23 A.Figure 23 A illustrates the FF performance variable time-sequence curve chart over time that puts on controll plant.Figure 23 B is the temperature y time-sequence curve chart over time that controll plant is shown.Figure 23 A illustrates FF performance variable [J/s] at ordinate, and at horizontal ordinate is shown the time [s].Figure 23 B illustrates the temperature y[K of controll plant at ordinate] and at horizontal ordinate is shown the time [s].In addition, with reference to Figure 23 B, solid line represents the temperature (temperature variation) of the controll plant when controll plant not being applied FF performance variable shown in Figure 23 A, and dotted line represents the temperature (temperature variation) of the controll plant when the FF performance variable that controll plant applied shown in Figure 23 A.

Obvious from Figure 23 B, (in present embodiment) was than little when the FF performance variable is not applied in controll plant when the temperature variation of controll plant was applied in controll plant at the FF performance variable.More specifically, when controll plant was not applied in the FF performance variable, the temperature variation of controll plant was about 2[K], and the temperature variation of controll plant is reduced to noise level when controll plant is applied in the FF performance variable.

By this operation, in the present embodiment, based on the result who when controll plant being applied FF performance variable (benchmark performance variable), the response (temperature) of controll plant is measured, acquisition puts on the FF performance variable of controll plant constantly at each, and not to controll plant (its temperature characterisitic) modeling.Therefore, in the present embodiment, can be in the situation that does not produce modeling load or modeling error the temperature of pin-point accuracy ground control controll plant.

The embodiment of the method for＜manufacturing article 〉

Method according to the manufacturing article of present embodiment is suitable for making various article, comprises micro element (such as semiconductor devices) and the element with microstructure.The method can comprise uses flat plate printing apparatus (such as above-mentioned exposure device) to come in the upper step (carrying out the step of exposure, impression or the drawing on object) that forms pattern of object (substrate that for example, has anticorrosive additive material (such as Photoresist or resin) in its surface).The method can also comprise that processing (for example developing or etching) forms the step of figuratum object in the above in forming step.The method can comprise follow-up known steps (for example, oxidation, film forming, vapor deposition, doping, complanation, etching, resist are removed, cut, engaged and packing) in addition.According to the method for the manufacturing article of present embodiment more favourable than conventional method aspect at least one of performance, quality, throughput rate and the manufacturing cost of article.

Notice that above-mentioned flat plate printing apparatus is not limited to above-mentioned exposure device, but can be imprinting apparatus or charged particle plotting unit.

Each aspect of the present invention can also be by following realization: read and the program of executive logging on memory device with the system of the function of carrying out above-described embodiment or the computing machine (perhaps devices such as CPU or MPU) of device, and by for example being read by the computing machine of system or device and the program of executive logging on memory device carried out the method for its step with the function of carrying out above-described embodiment.For this reason, for example provide program via network or from the various types of recording mediums (for example, computer-readable medium) as memory device to computing machine.

Although described the present invention with reference to exemplary embodiment, be to be understood that to the invention is not restricted to disclosed exemplary embodiment.The scope of following claim will be endowed the widest explanation to comprise all such modifications and the structure that is equal to or function.

Claims (10)

1. a control device comprises feedforward controller, and this feedforward controller is configured to carry out the feedforward control of controll plant, and described control device is configured to:

Acquisition is by the first response data sequence of the controll plant that controll plant applied the first performance variable and measure,

If suppose that the second response data sequence of the controll plant that the second performance variable data sequence that obtains by the gain of the first performance variable be multiply by respectively as the variable that can change is in time put on controll plant and will obtain is represented as the first response data sequence and as the linear combination of the gain of the coefficient of linear combination, determine gain so that the difference between the second response data sequence and the target data sequence falls in the permission, and

Feedforward controller is configured to generate feedforward operation variable data sequence for controll plant based on determined gain.

2. control device according to claim 1, wherein, described control device is configured to obtain the first response data sequence for a plurality of the first response data sequences that obtain respectively by constantly controll plant being applied the first performance variable in difference.

3. control device according to claim 1, wherein, the control variable of described control device comprises the position of controll plant.

4. control device according to claim 3, wherein, gain is determined in each zone in a plurality of zones that described control device is configured to move for controll plant.

5. control device according to claim 1, wherein, the control variable of described control device comprises the temperature of controll plant.

6. control device according to claim 1, wherein, described control device be configured to for the response characteristic of controll plant mutually each service condition in a plurality of service conditions of different controll plants determine to gain.

7. control device according to claim 1, wherein, described control device comprises the memory storage of the coefficient of the linear combination that is configured to store a plurality of component data sequences and is used for described a plurality of component data sequences, and described a plurality of component data sequences are used for obtaining forward direction performance variable data sequence by the linear combination of a plurality of component data sequences.

8. control device according to claim 1, wherein, described control device comprises feedback controller, described feedback controller is configured to carry out the FEEDBACK CONTROL of controll plant in order to reduce error between the response of target data and controll plant.

9. one kind forms the flat plate printing apparatus of pattern at object, and described flat plate printing apparatus comprises:

Adjustment equipment is configured to adjust the state of object; With

The control device of definition is configured to control the adjustment equipment as controll plant in the claim 1.

10. method of making article, described method comprises:

Use flat plate printing apparatus to form pattern at object; And

Process the object that has formed pattern on it and make article,

Wherein, described flat plate printing apparatus comprises:

Adjustment equipment is configured to adjust the state of object; With

Control device is configured to control the adjustment equipment as controll plant,

Wherein, described control device comprises the feedforward controller of the feedforward control that is configured to carry out controll plant, and described control device is configured to:

Acquisition is by the first response data sequence of the controll plant that controll plant applied the first performance variable and measure,

If suppose that the second response data sequence of the controll plant that the second performance variable data sequence that obtains by the gain of the first performance variable be multiply by respectively as the variable that can change is in time put on controll plant and will obtain is represented as the first response data sequence and as the linear combination of the gain of the coefficient of linear combination, determine gain so that the difference between the second response data sequence and the target data sequence falls in the permission, and

Feedforward controller is configured to generate feedforward operation variable data sequence for controll plant based on determined gain.

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